GATE EC 2026 Set 1 — Question 21
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Electromagnetics → Antennas → Effective Aperture
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Question
Consider the Friis' transmission equation , where and are the received and the transmitted powers, respectively. and are the gain of transmitting and receiving antennas, respectively, is the distance between the transmitting and receiving antennas, and is the wavelength in free space.
Given: , m and dBm.
Choose the distance (), in km, from the following options at which the received power, dBm?
Given: , m and dBm.
Choose the distance (), in km, from the following options at which the received power, dBm?
Correct answer
(B) (15)/(2π)
Solution
The Friis' transmission equation is given by:
We are given the following values:
For dBm:
For dBm:
Now, rearrange the Friis' equation to solve for the distance :
Substitute the numerical values:
The question asks for the distance in kilometers (km). To convert meters to kilometers, divide by :
This result matches option (B).The final answer is
We are given the following values:
- Transmitting antenna gain,
- Receiving antenna gain,
- Wavelength, m
- Transmitted power, dBm
- Received power, dBm
For dBm:
For dBm:
Now, rearrange the Friis' equation to solve for the distance :
Substitute the numerical values:
The question asks for the distance in kilometers (km). To convert meters to kilometers, divide by :
This result matches option (B).The final answer is
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